Question

Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other?

A. yes, because a difference in mean rating of –2.3 or less occurred only 5 out of 200 times, meaning the difference is statistically significant, and there is convincing evidence that a is more effective than b.
B. yes, because a difference in mean rating of –2.3 or less occurred only 5 out of 200 times, meaning the difference is statistically significant, and there is convincing evidence that b is more effective than a.
C. no, because a difference in mean rating of –2.3 or more occurred 195 out of 200 times, meaning the difference is not statistically significant, and there is not convincing evidence that one brand is better than the other.
D. no, because a difference in mean rating of –2.3 or less only occurred 5 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.

Answer 1

A difference in mean rating of -2.3 or less occurring only 5 out of 200 times indicates the difference is statistically significant. Therefore, there is convincing evidence that detergent a is more effective than detergent b.

Step-by-step explanation:

To determine if there is convincing evidence that one detergent is better than the other using a dotplot and the difference in mean ratings from the samples, we need to look at the significance level and the frequency of occurrence of the observed difference.

If a difference in mean rating of – 2.3 or less occurred only 5 out of 200 times, this means that such an extreme or more extreme difference would happen by chance only 5 out of 200 times, or 2.5% of the time, which is less than the commonly used significance level of 5%. Therefore, we would consider this difference to be statistically significant.

The correct answer is: A. Yes, because a difference in mean rating of – 2.3 or less occurred only 5 out of 200 times, meaning the difference is statistically significant, and there is convincing evidence that a is more effective than b.